Despite the visitors arriving in Somerset 21 places ahead of Town, it was Darren Way’s side who were unlucky to not have won the game as Plymouth were put under heavy pressure, particularly in the first half.
Walsh was at the centre of it all, and was named the sponsors man of the match award for the second time in four days after superb performances against Argyle and previous opponents Portsmouth.
The young midfielder waxed lyrical about the team’s performance and told media after the game, “It was a great game for us. First half we were on top, we were expecting to score to put us a goal ahead, but we were on top all game and all we needed was one goal.
“After the performance against Portsmouth, coming up against Plymouth who are one of the best teams in the league, we knew that we needed to be fired up from the off.
“I think that the last few weeks we've been like that but now we need to start gaining more points.”
Walsh, who has made nine appearances since arriving on loan from Premier League side Everton, played all but five minutes of injury time in the double header at home.
And the 18 year old explained that the team were delighted with not just the two draws against two promotion-hopefuls, but the fact the Glovers are now outside the drop zone.
“They're two of the best teams in the league,” explained Walsh.
“But with the gaffer coming in, Huish Park is a tough place to come with the form that we're in.
“All the teams around are losing games and we're dragging them closer, so any points are vital.
“It's a great feeling (to be outside the relegation places), that's what we've been talking about all week and all season. It'd mean the world to stay up and keep playing league football, and I think all the lads know that themselves and we're going to keep performing to make sure we don't go down.”
Darren Way’s men now face a trip to London in a basement battle with Dagenham and Redbridge, and three points in the East End would put nine points between the Glovers and the Victoria Road outfit.
And Walsh explained they would still need the same fighting spirit shown in the last two games if they were to emerge victorious, saying “It's a different type of team, as they're bottom of the league.
“But we'll still go into it with the same passion and fired up for it like we have the last two games against the big teams, and I think we can get the three points against Dagenham.”
With the amount of champagne bottles that the youngster has received piling up and up, Walsh denied that he had drunk them, but explained they’re being well looked after.
“I just give them to my dad to keep hold of them!” he said.
“I'm just made up for all the lads, it's a brilliant team performance from all the lads, and we want to keep it going.”